Independent solution

How to solve this Interest Rate Valuation question

Setup

Setup

First determine the contract fund remaining after four claim payments.

F4=500(1.05)4−100s4‾∣ 0.05=176.74F_4=500(1.05)^4-100s_{\overline4|\,0.05}=176.74

Model

Model

The insurer retains one-quarter of that remainder, in addition to its year-two fee, against the time-zero expense.

CFinsurer=(−100, 125 at 2, 44.19 at 4)CF_{\rm insurer}=(-100,\ 125\text{ at }2,\ 44.19\text{ at }4)

Compute

Compute

Accumulating all insurer cash flows to year four produces a quadratic in one plus i squared; the positive root gives 24%.

100(1+i)4−125(1+i)2−44.19=0100(1+i)^4-125(1+i)^2-44.19=0

Answer

Answer

The insurer's yield is 24%, corresponding to choice B.

i=24%(B)\boxed{i=24\%\quad\text{(B)}}

Calculator reproduction

BA II Plus keystrokes

Check END/BGN, period, sign, TVM, and cash-flow setup

  1. CF; 2nd CLR WORK; CF0=-100; C01=0; F01=1; C02=125; C03=0; F03=1; C04=44.19; IRR; CPTIRR = 24.00The worksheet period is one year; the initial investment is negative and receipts are positive.